Stabilizer type Z16

Acting group: 𝔇12
There are exactly 8 groups in this conjugacy class.
The group order is 6.
(T0,S0),
(T4,S4),
(T8,S8),
(I,SR) ∘ P,
(T4I,S5R) ∘ P,
(T8I,S9R) ∘ P.
(T0,S0),
(T4,S4),
(T8,S8),
(TI,S2R) ∘ P,
(T5I,S6R) ∘ P,
(T9I,S10R) ∘ P.
(T0,S0),
(T4,S4),
(T8,S8),
(T2I,S3R) ∘ P,
(T6I,S7R) ∘ P,
(T10I,S11R) ∘ P.
(T0,S0),
(T4,S4),
(T8,S8),
(T3I,S4R) ∘ P,
(T7I,S8R) ∘ P,
(T11I,R) ∘ P.
(T0,S0),
(T4,S8),
(T8,S4),
(T0,S0) ∘ P,
(T4,S8) ∘ P,
(T8,S4) ∘ P.
(T0,S0),
(T4,S8),
(T8,S4),
(T,S11) ∘ P,
(T5,S7) ∘ P,
(T9,S3) ∘ P.
(T0,S0),
(T4,S8),
(T8,S4),
(T2,S10) ∘ P,
(T6,S6) ∘ P,
(T10,S2) ∘ P.
(T0,S0),
(T4,S8),
(T8,S4),
(T3,S9) ∘ P,
(T7,S5) ∘ P,
(T11,S) ∘ P.

Where
S=T=(1,2,3,4,5,6,7,8,9,10,11,12) ,
R=(6,7)(5,8)(4,9)(3,10)(2,11)(1,12) ,
I=(7)(6,8)(5,9)(4,10)(3,11)(2,12)(1) ,
F=Q=(10)(8,12)(7)(5,9)(4)(3,11)(2,6)(1) .

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